How can a 16 year old get a passport if mother is in jail and father is in mexico?

i read everything at travel.state.gov. but it doesnt help me. It says For All Minors Ages 16 & 17:

Each minor child shall appear in person.
For security reasons, parental consent may be requested.
If your child does not have identification of his/her own, you need to accompany your child and
present identification.
What gets me is the for security reasons, parental consent may be requested.
well the mother is in jail and the father is in mexico.

so are they going to ask for parental consent ?

The site you mention has a link to a list of 9000 places (incl. many local libraries) that accept applications. Take your documents (birth certificate, photos, application, etc.) there and see what they say.

Addition: I don't know if you can tell in advance what they'll ask for. Make a try. If they want something you don't have, we can go from there.

can a 16 year old not just apply for a passport ??

you need a legal guardian to act as a parent.

Not going to happen.

your legal guardian signs where your parent would sign